Determination of the atomic structure of solid surfaces typically depends on comparison of measured properties with simulations based on hypothesized structural models. For simple structures, the models may be guessed, but for more complex structures there is a need for reliable theory-based search algorithms. So far, such methods have been limited by the combinatorial complexity and computational expense of sufficiently accurate energy estimation for surfaces. However, the introduction of machine learning methods has the potential to change this radically. Here, we demonstrate how an evolutionary algorithm, utilizing machine learning for accelerated energy estimation and diverse population generation, can be used to solve an unknown surface structure-the (4×4) surface oxide on Pt3 Sn(111)-based on limited experimental input. The algorithm is efficient and robust, and should be broadly applicable in surface studies, where it can replace manual, intuition based model generation.

Center for Interstellar Catalysis Department of Physics and Astronomy Aarhus University 8000 Aarhus Denmark

Department of Surface and Plasma Science Faculty of Mathematics and Physics Charles University 180 00 Prague 8 Czech Republic

Div of Synchrotron Radiation Research Lund University 22100 Lund Sweden

Institute of Applied Physics TU Wien 1040 Vienna Austria

Materials Science and Applied Mathematics Malmö University 20506 Malmö Sweden

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Burch R., J. Catal. 1981, 71, 348–359.

Cortright R. D., Hill J. M., Dumesic J. A., Catal. Today 2000, 55, 213–223.

Coloma F., Sepúlveda-Escribano A., Fierro J., Rodríguez-Reinoso F., Appl. Catal. A 1996, 136, 231–248.

Moscu A., Veyre L., Thieuleux C., Meunier F., Schuurman Y., Catal. Today 2015, 258, 241–246.

Arenz M., Stamenkovic V., Blizanac B., Mayrhofer K., Markovic N., Ross P., J. Catal. 2005, 232, 402–410. PubMed

Lamy C., Rousseau S., Belgsir E., Coutanceau C., Léger J.-M., Electrochim. Acta 2004, 49, 3901–3908.

Batzill M., Beck D. E., Koel B. E., Appl. Phys. Lett. 2001, 78, 2766–2768.

Batzill M., Beck D. E., Koel B. E., Phys. Rev. B 2001, 64, 245402.

Batzill M., Kim J., Beck D. E., Koel B. E., Phys. Rev. B 2004, 69, 165403.

Atrei A., Bardi U., Rovida G., Torrini M., Hoheisel M., Speller S., Surf. Sci. 2003, 526, 193–200.

Hoheisel M., Speller S., Heiland W., Atrei A., Bardi U., Rovida G., Phys. Rev. B 2002, 66, 165416.

Zheng J., Busch M., Artiglia L., Skála T., Rossmeisl J., Agnoli S., Adv. Mater. Interfaces 2019, 6, 1801874.

Oganov A., Pickard C., Zhu Q., Needs R., Nat. Rev. Mater. 2019, 4, 331–348.

Kirkpatrick S., Gelatt C. D., Vecchi M. P., Science 1983, 220, 671. PubMed

Pickard C. J., Needs R. J., J. Phys. Condens. Matter 2011, 23, 053201. PubMed

Wales D. J., Doye J. P. K., J. Phys. Chem. A 1997, 101, 5111–5116.

Amsler M., Goedecker S., J. Chem. Phys. 2010, 133, 224104. PubMed

Laio A., Parrinello M., Proc. Natl. Acad. Sci. USA 2002, 99, 12562–12566. PubMed PMC

Earl D. J., Deem M. W., Phys. Chem. Chem. Phys. 2005, 7, 3910–3916. PubMed

Wang Y., Lv J., Zhu L., Ma Y., Phys. Rev. B 2010, 82, 094116.

Oganov A. R., Glass C. W., J. Chem. Phys. 2006, 124, 244704. PubMed

Abraham N. L., Probert M. I. J., Phys. Rev. B 2006, 73, 224104.

Vilhelmsen L. B., Hammer B., J. Chem. Phys. 2014, 141, 044711. PubMed

Woodley S., Day G., Catlow R., Philos. Trans. R. Soc. London Ser. A 2020, 378, 20190600. PubMed

Sierka M., Todorova T. K., Sauer J., Kaya S., Stacchiola D., Weissenrieder J., Shaikhutdinov S., Freund H.-J., J. Chem. Phys. 2007, 126, 234710. PubMed

Merte L. R., Jørgensen M. S., Pussi K., Gustafson J., Shipilin M., Schaefer A., Zhang C., Rawle J., Nicklin C., Thornton G., Lindsay R., Hammer B., Lundgren E., Phys. Rev. Lett. 2017, 119, 096102. PubMed

Zakaryan H., Kvashnin A., Oganov A., Sci. Rep. 2017, 7, 10357. PubMed PMC

Kolsbjerg E. L., Peterson A. A., Hammer B., Phys. Rev. B 2018, 97, 195424.

Deringer V., Proserpio D., Csanyi G., Pickard C., Faraday Discuss. 2018, 211, 45–59. PubMed

Tong Q., Xue L., Lv J., Wang Y., Ma Y., Faraday Discuss. 2018, 211, 31–43. PubMed

Bisbo M. K., Hammer B., Phys. Rev. Lett. 2020, 124, 086102. PubMed

D. Arthur, S. Vassilvitskii in Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, USA, of SODA'07, pp. 1027–1035.

Jørgensen M. S., Groves M. N., Hammer B., J. Chem. Theory Comput. 2017, 13, 1486–1493. PubMed

Y. Wang, C. Dang, H. Li, L. Han, J. Wei in 2009 IEEE Congress on Evolutionary Computation, pp. 2927–2933.

Yuan Y., Xu H., Wang B., Yao X., IEEE Trans. Evol. Comput. 2016, 20, 16–37.

Zhang X., Tian Y., Cheng R., Jin Y., IEEE Trans. Evol. Comput. 2018, 22, 97–112.

Cheng B., Griffiths R.-R., Wengert S., Kunkel C., Stenczel T., Zhu B., Deringer V. L., Bernstein N., Margraf J. T., Reuter K., Csanyi G., Acc. Chem. Res. 2020, 53, 1981–1991. PubMed

Stamenković V. R., Arenz M., Lucas C. A., Gallagher M. E., Ross P. N., Marković N. M., J. Am. Chem. Soc. 2003, 125, 2736–2745. PubMed

Sokolović I., Reticcioli M., Čalkovský M., Wagner M., Schmid M., Franchini C., Diebold U., Setvín M., Proc. Natl. Acad. Sci. USA 2020, 117, 14827–14837. PubMed PMC

Seko A., Togo A., Oba F., Tanaka I., Phys. Rev. Lett. 2008, 100, 045702. PubMed

Suzuki K., Hanaya T., Sato R., Minato T., Yamaguchi K., Mizuno N., Chem. Commun. 2016, 52, 10688–10691. PubMed

Batzill M., Chaka A. M., Diebold U., Europhys. Lett. 2004, 65, 61–67.

Atrei A., Bardi U., Rovida G., Torrini M., Zanazzi E., Ross P. N., Phys. Rev. B 1992, 46, 1649–1654. PubMed

Bortoluzzi M., Ceriotti A., Ciabatti I., Della Pergola R., Femoni C., Carmela Iapalucci M., Storione A., Zacchini S., Dalton Trans. 2016, 45, 5001–5013. PubMed

Jennings M. C., Schoettel G., Roy S., Puddephatt R. J., Organometallics 1991, 10, 580–586.

Deringer V. L., Bernstein N., Csányi G., Ben Mahmoud C., Ceriotti M., Wilson M., Drabold D. A., Elliott S. R., Nature 2021, 589, 59–64. PubMed

Smith J. S., Nebgen B. T., Zubatyuk R., Lubbers N., Devereux C., Barros K., Tretiak S., Isayev O., Roitberg A. E., Nat. Commun. 2019, 10, 2903. PubMed PMC

Van der Oord C., Dusson G., Csányi G., Ortner C., Mach. Learn.: Sci. Technol. 2020, 1, 015004.

Mortensen H. L., Meldgaard S. A., Bisbo M. K., Christiansen M.-P. V., Hammer B., Phys. Rev. B 2020, 102, 075427.